Feynman's Wobbling Plate

In his eccentric collection of autobiographical stories (see reference), Richard Feynman recounts: "I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster than the wobbling. I had nothing to do, so I start figuring out the motion of the rotating plate. I discovered that when the angle is very slight, the medallion rotates twice as fast as the wobble rate—two to one. It came out of a complicated equation! I went on to work out equations for wobbles. Then I thought about how the electron orbits start to move in relativity. Then there's the Dirac equation in electrodynamics. And then quantum electrodynamics. And before I knew it… the whole business that I got the Nobel prize for came from that piddling around with the wobbling plate." A replica of the Cornell plate is now part of an exhibit marking the centennial of the Nobel Prize.

Actually, Feynman misremembered (or was being mischievous): the factor of 2 actually goes the other way. In the Details section below, the motion of the plate is derived using Euler's equations for a rigid body.

In this Demonstration, the trajectory of the plate is shown in slow motion. The initial conditions to be chosen are , the inclination of the plate's symmetry axis to the vertical and , the rate of rotation about this axis. It is found that the wobble rate is actually slightly more than twice the rotation rate. The ratio approaches 2 as , but, at the same time, the wobble amplitude decreases.